1. Field of the Invention
The present invention relates to a high speed numerical integration system and method, and in particular to a high speed numerical integration system and method for converting a multi-dimensional sequence into a one-dimensional characteristic value, and for calculating a weighted average for correction.
2. Related Art
Conventional, well known variance reduction methods for Monte Carlo (MC) calculations using a pseudo-random number are as follows.
Antithetic Variable Method
A random sequence and a sequence having the same absolute value but with an opposite sign are joined together to obtain an antithetic distribution of variables in order to reduce variance.
Moment Matching Method
An average and a variance are acquired from a random sequence that has been generated, and the values of the random numbers being corrected so that an anticipated average and variance are obtained.
Since a generated random number is processed using these methods, a problem concerning the autocoorelation has arisen.
In addition, since according to the moment matching method all the random numbers that have been generated must be stored, this method is not practical for high-order dimensions.
Furthermore, these methods by which the locations of points are altered are not suitable for a sequence, such as an LDS (low-discrepancy sequence) that provides biasless sample points.